Question

One summer you charge \(\$ 20\) to mow a lawn and \(\$ 10\) to trim bushes. You want to make \(\$ 300\) in one week. An algebraic model for your earnings is \(20 x+10 y=300,\) where \(x\) is the number of lawns you mow and \(y\) is the number of bushes you trim. If you do not trim any bushes during the week, how many lawns will you have to mow to earn \(\$ 300 ?\)

Short answer

When no bushes are trimmed, you have to mow 15 lawns to earn $300.

Step-by-step solution

Understand the problem

The problem provides an equation that represents the earnings generated by mowing lawns and trimming bushes. The goal is to find out the number of lawns (x) that need to be mowed, when no bushes (y) are trimmed, to reach an earnings target of $300.

Substitute the given values into the equation

Now we take the equation, '20x + 10y = 300', and replace 'y' with '0', as we are asked to consider the situation where no bushes are trimmed. This results in the equation: '20x + 10*0 = 300', which simplifies to '20x = 300'.

Solve for x

To solve for 'x', we divide both sides of the equation '20x = 300' by '20'. This results in 'x = 300 / 20'.

Calculate the final result

After performing the division, we find that 'x = 15'. This means that 15 lawns need to be mowed to reach the earnings target of $300 when no bushes are trimmed.